FIND PROBABILITY USING XLSTAT HOW TO

Can you figure out how to calculate that probability given the above information? Our ultimate goal as a random packer is that we’d like to have two tan pants and two blue shirts in our suitcase. Related post: Using Permutations to Calculate Probabilities and Using Combinations to Calculate Probabilities Bonus Example Problem! We have the two joint probabilities of 0.066 for two tan pants and 0.05 for two blue shirts. Using the same approach, we get the following: The joint probability of drawing two pairs of tan pants is 0.066, which equals the probability of the first pair of tan pants multiplied by the conditional probability of the second pair of tan pants given that the first pair was tan.Īnd, for the shirts, we start with four blue shirts out of 16 total shirts. The probability of the second pair being tan (T2) is 2/9 = 0.22. Consequently, the probability of the first pair of pants being tan (event T1) is 0.30. We begin with 10 pairs of pants, three of which are tan. We’ll start by treating this as two sets of dependent events, one for pants and the other for shirts.

We’re hoping for two pairs of tan pants and two blue shirts. Imagine that we’re packing for a short trip and randomly select two pairs of pants and two pairs of shirts to include in our suitcase. Let’s go back to the pants and shirt example. Or, the joint probability of drawing two consecutive hearts equals the probability of the first heart multiplied by the probability of the second heart given that the first card was a heart.Ġ.25 * 0.235 = 0.059 Dependent Events: Tan Pants and Blue Shirts Example The dependent probability of drawing that second heart (event H2) is now 12/51 = 0.235. If you draw a heart (event H1), that changes the probability of drawing another heart. Initially, the deck has 13 hearts out of its 52 cards (13/52 = 0.25). Suppose you are interested in the probability of drawing hearts on two consecutive draws. As you draw cards, it affects the probability of the next card you can draw. The classic example for dependent events is drawing cards from a deck of cards without replacement. Related post: Using Contingency Tables to Calculate Probabilities Examples of the General Multiplication Rule The general multiplicative rule allows you to factor in the other event, as you will see in the next two examples! That’s just another way of saying that event A occurring affects the probability of event B (i.e., they’re dependent events). However, for dependent events, P(B|A) ≠ P(B). Consequently, this rule becomes equivalent to the specific multiplicative rule for independent events. That’s the very definition of independent events. In the context of independent events, P(B|A) = P(B) because event A occurring does not impact event B’s probability. Why can you use the general form for both independent and dependent events? In the notation, focus on P(B|A), which is the conditional probability that event B occurs given that event A occurred. It works for both independent and dependent events, whereas the specific rule is valid only for independent events. The difference between the general and specific rules is, unsurprisingly, that you can use the general rule more generally. Or, the joint probability of A and B occurring equals the probability of A occurring multiplied by the conditional probability of B occurring given that A occurred. Using standard notation, the general multiplication rule is the following: When you have dependent events, you must use the general multiplication rule because it allows you to factor in how the occurrence of event A affects the likelihood of event B. Use the general multiplication rule to calculate joint probabilities for either independent or dependent events.

The likelihood of getting your preferred combination is low! You might want to drink some coffee to increase your chances! General Multiplication Rule Or, the joint probability of randomly selecting a pair of tan pants and a blue shirt equals 0.075, which is the probability of tan pants multiplied by the probability of a blue shirt. Using the specific multiplication rule for these independent events:

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