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20% of kids like spinach, 88% like potatoes and 20% like broccoli. You also know

ID: 2936471 • Letter: 2

Question

20% of kids like spinach, 88% like potatoes and 20% like broccoli. You also know that 10% like spinach and potatoes but not broccoli, 5% like spinach and broccoli but not potatoes, 7% like potatoes and broccoli but not spinach and 2% of students like only spinach (no potatoes and no broccoli). Draw Venn diagram and answer the questions.

a. What percentage of students like all spinach, broccoli and potatoes?

b. What percentage of students like only potatoes (no spinach, no broccoli)?

c. How many students like broccoli only if you know that total number of students is 100?

Explanation / Answer

A) P(s) = 0.2

P(P) = 0.88

P(B) = 0.2

P(only S and P) = 0.1

P(only S and B) = 0.05

P(only P and B) = 0.07

P(only s) = 0.02

A) P (S and P and B) = P(S) - (P(only s) + P(s and B) + P(S and P))

= 0.2 - (0.02 + 0.05 + 0.1)

= 0.2 - 0.17 = 0.03

B) P(only P) = P(P) - (P(S and P) + P(P and B) + P(S and P and B))

= 0.88 - (0.1 + 0.07 + 0.03)

= 0.88 - 0.2 = 0.68

C) P(only B) = P(B) - (P(S and B) + P(B and P) + P(S and P and B))

= 0.2 - (0.05 + 0.07 + 0.03)

= 0.2 - 0.15 = 0.05

Total no of students like broccoli = 100 * 0.05 = 5