Question

PLEASE WRITE LEGIBLE

Answer 1

Let B1 shows the event that guy from couple A forgets to bring the money and G1 shows the event that girl from couple A forgets to bring the money. So we have

P(B1) = 0.10, P(G1) = 0.10

Let B2 shows the event that guy from couple B forgets to bring the money and G2 shows the event that girl from couple B forgets to bring the money. So we have

P(B2) = 0.07, P(G2) = 0.07

By the complement rule

P(B1') =1-P(B1) = 0.90, P(G1') =0.90, P(B2') = 0.93, P(G2') = 0.93

Now the ways exactly two individuals forgot to bring money are

B1 G1 B2' G2', B1 G1' B2 G2', B1' G1 B2 G2', B1 G1' B2' G2, B1' G1 B2' G2, B1' G1' B2 G2

So the probability that  exactly two individuals forgot to bring money is

P(exactly two forget) =P(B1 G1 B2' G2')+P( B1 G1' B2 G2')+P( B1' G1 B2 G2')+P( B1 G1' B2' G2)+P( B1' G1 B2' G2)+P( B1' G1' B2 G2) = 0.10 *0.10 *0.93 *0.93 + 0.10*0.90*0.07*0.93 + 0.90*0.10*0.07*0.93 + 0.10*0.90*0.90*0.07 + 0.90*0.10*0.93*0.07 + 0.90*0.90*0.07*0.07 = 0.035865

And the probability that two guys forgot to bring money is

P(exactly two forget and two guys forget) = P( B1 G1' B2 G2') = 0.10 * 0.90 * 0.07* 0.93 = 0.005859

Hence, the required probability is

P( two guys forget | exactly two forget) =P(exactly two forget and two guys forget) /P(exactly two forget) = 0.005859 / 0.035865 = 0.1634

Answer: 0.1634