Question

The tree diagram below shows the distribution of cars sold and whether each type got upgrades or not. Find the Probability of a random car getting an upgrade.

Answer 1

To find the probability of a random car getting an upgrade, we need to sum the probabilities of each branch where the car gets an upgrade.

Let's denote the events as follows:
A: Car sold is type A
B: Car sold is type B
C: Car sold is type C
D: Car sold is type D
U: Car gets an upgrade
NU: Car does not get an upgrade

From the tree diagram, we have the following probabilities:
P(A) = 0.2, P(B) = 0.3, P(C) = 0.4, P(D) = 0.1
P(U|A) = 0.8, P(NU|A) = 0.2
P(U|B) = 0.7, P(NU|B) = 0.3
P(U|C) = 0.6, P(NU|C) = 0.4
P(U|D) = 0.5, P(NU|D) = 0.5

Now we can calculate the probability of a random car getting an upgrade:
P(U) = P(A and U) + P(B and U) + P(C and U) + P(D and U)
= P(A) * P(U|A) + P(B) * P(U|B) + P(C) * P(U|C) + P(D) * P(U|D)
= (0.2 * 0.8) + (0.3 * 0.7) + (0.4 * 0.6) + (0.1 * 0.5)
= 0.16 + 0.21 + 0.24 + 0.05
= 0.66

Therefore, the probability of a random car getting an upgrade is 0.66 or 66%.