Question

*Give all probabilities to four decimal places.

Bowl #1 contains 2 grape candies, 7 lemon candies, 8 cherry candies and 3 raspberry candies.

Bowl #2 contains 6 grape candies, 5 lemon candies, 2 cherry candies and 7 raspberry candies.

(c) What is the probability that the two selected candies are the same flavour?
(d) What is the probability that the two selected candies are different colours?

(e) What is the probability that the first selected candy is lemon or that the second selected candy is cherry?

(f) Let X be the number of grape candies that are selected. Find the p

Answer 1

*So it doesn't explicitly state, but I'm assuming that where you say 'two selected candies' you mean one from each bowl

c) We want to calculate P(both are same)

P(both are the same) = P(G1 and G2) + P(L1 and L2) + P(C1 and C2) + P(R1 and R2)
where G1 := Grape from bowl one

P(A and B)=P(A)xP(B)
P(G1 and G2) = P(G1)xP(G2) = 2/20 x 6/20 = 12/400
P(L1 and L2) = P(L1)xP(L2) = 7/20 x 5/20 = 35/400
P(C1 and C2) = P(C1)xP(C2) = 8/20 x 2/20 = 16/400
P(R1 and R2) = P(R1)xP(R2) = 3/20 x 7/20 = 21/400

I'm assuming you can calculate basic probabilities e.g. P(G1), but I'll do the first one anyway.
P(G1) = number of grape/total number of sweets = 2/20 = 1/10 = 0.1 (I'm going to leave things in fractions but if you prefer decimals then go ahead)

P(both are the same) = 12/400 + 35/400 + 16/400 + 21/400 = 84/400 = 0.21 (0.2100 if you want but I think that's unnecessary)

Final Answer = 0.21

Answer 2

d) P(both are different) = 1 - P(both are same)
This is because these events are exhaustive, as all outcomes fall in to one of these two categories.

Therefore:
P(both are different) = 1 - 0.21 (Answer taken from above)
= 0.79

Final Answer = 0.79