Thomas planted tomatoes, peppers, and green beans. The probability that the tomato plant will produce tomatoes is .8, the probability that the pepper plant will produce peppers is .4 and the probability that the green bean plant will produce green beans is .7. Assuming that these events are all independent of one another, what is the probability that Thomas will get tomatoes and peppers , but NOT green beans?
So I must set it up as P (T∩P∩Gcomplement)? Is just p(T) * p(P) ignoring p(G) or is it something else? I forgot how to handle complements.
Or 1- p(t)*p(p)?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
.8 * .4 * (1-.7) = ?
To find the probability of Thomas getting tomatoes and peppers but not green beans, we need to find the product of the probabilities of each event happening.
Let's break down the problem step by step.
Step 1: Find the probability of getting tomatoes (T). The probability of the tomato plant producing tomatoes is given as 0.8.
P(T) = 0.8
Step 2: Find the probability of getting peppers (P). The probability of the pepper plant producing peppers is given as 0.4.
P(P) = 0.4
Step 3: Find the probability of not getting green beans (G'). Consider that the probability of the green bean plant producing green beans is given as 0.7. To find the probability of not getting green beans, subtract this probability from 1.
P(G') = 1 - P(G)
P(G') = 1 - 0.7
P(G') = 0.3
Step 4: Multiply the probabilities of each event happening:
P(T ∩ P ∩ G') = P(T) * P(P) * P(G')
P(T ∩ P ∩ G') = 0.8 * 0.4 * 0.3
P(T ∩ P ∩ G') = 0.096
Therefore, the probability that Thomas will get tomatoes and peppers but not green beans is 0.096 or 9.6%.