a spinner has 10 equally sized sections, 1 of which is yellow and 9 of which are red. the spinner is spun…

a spinner has 10 equally sized sections, 1 of which is yellow and 9 of which are red. the spinner is spun and, at the same time, a fair coin is tossed. what is the probability that the spinner lands on red and the coin toss is tails? do not round your answer.

a spinner has 10 equally sized sections, 1 of which is yellow and 9 of which are red. the spinner is spun and, at the same time, a fair coin is tossed. what is the probability that the spinner lands on red and the coin toss is tails? do not round your answer.

Answer

Explanation:

Step1: Calculate probability of spinner landing on red

The spinner has 10 sections, 9 of which are red. So the probability of landing on red, $P(R)=\frac{9}{10}$.

Step2: Calculate probability of coin - toss being tails

A fair coin has 2 possible outcomes (heads or tails). So the probability of getting tails, $P(T)=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the spinner - spin and coin - toss are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(R\cap T)=P(R)\times P(T)$. $P(R\cap T)=\frac{9}{10}\times\frac{1}{2}=\frac{9}{20}$

Answer:

$\frac{9}{20}$