Question

Jack loves noodles , followed by dessert ice- cream
Jack's Mom cooks noodles once a week.
If she cooks noodles , then the probability jack gets ice-cream for dessert is $\frac{2}{3}$
If she doesn't cook noodles , then the probability jack gets ice-cream for dessert is $\frac{1}{4}$.
Using Tree diagram, Find the probability jack gets ice cream for dessert ?

• A. $\frac{8}{49}$
• B. $\frac{3}{14}$
• C. $\frac{13}{42}$
• D. $\frac{8}{7}$

Answer 1

Answer: (C)

$\frac{13}{42}$

The probability of Jacks mom cooking noodles is $\frac{1}{7}$

The probability of Jacks mom not cooking noodles is $\frac{6}{7}$

When she cooks noodles , then the probability of ice cream for dessert is $\frac{2}{3}$

So the probability that she cooks noodles and Jack gets ice cream for dessert is $\frac{1}{7}\times \frac{2}{3}=\frac{2}{21}$

When she does not cooks noodles , then the probability of ice cream for dessert is $\frac{1}{4}$

So the probability that she doesnt cooks noodles and Jack gets ice cream for dessert is $\frac{6}{7}\times \frac{1}{4}=\frac{3}{14}$

Therefore the probability that Jack gets ice cream for dessert is $\frac{2}{21}+\frac{3}{14}=\frac{13}{42}$