Given the probability of rain on any given day in March is 1/5, find the probablity that: It rains on March 10 and 12, but not on March 11th. This is supposed to be used with multiplication Rule 1:
P(A and B)= P(A)*P(B) cant figure it out, the answer is 4/125 and I have no clue how
I figured this out:
1/5 = rain
4/5= no rain
1/5*1/5*4/5 = 4/125
you want:
rain, no rain, rain
= (1/5)(4/5)(1/5) = 4/125
To solve this problem using the multiplication rule, you'll need to multiply the probabilities of each event occurring. Let's break down the steps:
1. Determine the probability of rain on March 10th: Given that the probability of rain on any given day in March is 1/5, the probability of rain on March 10th is also 1/5.
2. Determine the probability of no rain on March 11th: Since it doesn't rain on March 11th, the probability of no rain is 1 - (probability of rain). Therefore, the probability of no rain on March 11th is 1 - 1/5 = 4/5.
3. Determine the probability of rain on March 12th: Given that the probability of rain on any given day in March is 1/5, the probability of rain on March 12th is also 1/5.
4. Apply the multiplication rule: Now, we can use the multiplication rule to find the probability of all these events occurring together. According to rule 1, P(A and B) = P(A) * P(B). In this case, A represents rain on March 10th, and B represents rain on March 12th. Thus, the probability that it rains on March 10th and 12th is (1/5) * (4/5) * (1/5) = 4/125.
Therefore, the probability that it rains on March 10th and 12th, but not on March 11th, is 4/125.