Question

a coin and a six - sided die are tossed.
event a: the coin does not land on heads.
event b: the die lands on 4.
what is the probability that both events will occur?
p(a and b) = ?%
for independent events: p(a and b) = p(a) · p(b)
round your answer to the nearest whole percent

Explanation:

Step1: Find \( P(A) \)

A coin has 2 sides (heads, tails). Event A is coin not heads (so tails), so \( P(A)=\frac{1}{2} \).

Step2: Find \( P(B) \)

A six - sided die has 6 outcomes. Event B is die lands on 4, so \( P(B)=\frac{1}{6} \).

Step3: Calculate \( P(A\text{ and }B) \)

Since coin toss and die roll are independent, use \( P(A\text{ and }B)=P(A)\cdot P(B) \).
\( P(A)\cdot P(B)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12}\approx0.0833 \)

Step4: Convert to percentage

Multiply by 100: \( 0.0833\times100 = 8.33\%\approx8\% \)

Answer:

8%