a spinner is split into 3, red blue and yellow. you need to land on blue in the next 2 goes to win, what is the probability of losing?
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(win) = 1/3 * 1/3 = 1/9
P(lose) = 1 - 1/9 = 8/9
To determine the probability of losing, we first need to calculate the probability of landing on blue in the next two spins.
Since the spinner is split into three sections (red, blue, and yellow), there are three possible outcomes for each spin. So, the total number of possible outcomes for two spins is 3 x 3 = 9.
To calculate the probability of landing on blue in the next two spins, we need to determine the number of favorable outcomes (blue) out of the total possible outcomes.
The possible favorable outcomes are:
- Blue on the first spin and blue on the second spin (BB)
- Blue on the first spin and not blue on the second spin (BN)
- Not blue on the first spin and blue on the second spin (NB)
There is only one way to get BB, and similarly, there is one way to get NB or BN. So, the total number of favorable outcomes is 1 + 1 + 1 = 3.
Therefore, the probability of landing on blue in the next two spins is 3 favorable outcomes out of 9 total outcomes, which can be written as 3/9 or simplified to 1/3.
Since the question asks for the probability of losing, we can subtract the probability of winning (landing on blue in the next two spins) from 1 to find the probability of losing.
Probability of losing = 1 - Probability of winning
Probability of losing = 1 - 1/3
So, the probability of losing is 2/3 or approximately 0.667 (rounded to three decimal places).