There are 5 red tiles and 5 blue tiles with the letter A in a bag. There are also 6 red tiles and 4 blue tiles with the letter B in the bag. What is the probability that a randomly selected tile is blue or has the letter B?
To find the probability that a randomly selected tile is blue or has the letter B, we need to calculate the total number of blue tiles and the total number of tiles with the letter B, and then divide that by the total number of tiles in the bag.
Step 1: Calculate the total number of blue tiles:
There are 5 blue tiles with the letter A and 4 blue tiles with the letter B, so the total number of blue tiles is 5 + 4 = 9.
Step 2: Calculate the total number of tiles with the letter B:
There are 6 red tiles with the letter B and 4 blue tiles with the letter B, so the total number of tiles with the letter B is 6 + 4 = 10.
Step 3: Calculate the total number of tiles in the bag:
There are 5 red tiles with the letter A, 5 blue tiles with the letter A, 6 red tiles with the letter B, and 4 blue tiles with the letter B, so the total number of tiles in the bag is 5 + 5 + 6 + 4 = 20.
Step 4: Calculate the probability:
The probability of selecting a blue tile or a tile with the letter B is given by:
(Number of blue tiles + Number of tiles with the letter B) / Total number of tiles
Substituting the values we calculated:
(9 + 10) / 20 = 19 / 20
Therefore, the probability is 19/20 that a randomly selected tile is blue or has the letter B.
To find the probability of selecting a blue tile or a tile with the letter B, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
First, let's calculate the total number of blue tiles. We have 5 blue tiles with the letter A and 4 blue tiles with the letter B, so the total number of blue tiles is 5 + 4 = 9.
Next, let's calculate the total number of tiles with the letter B. We have 6 red tiles with the letter B and 4 blue tiles with the letter B, so the total number of tiles with the letter B is 6 + 4 = 10.
Now, let's calculate the total number of tiles in the bag. We have 5 red tiles with the letter A, 5 blue tiles with the letter A, 6 red tiles with the letter B, and 4 blue tiles with the letter B. Therefore, the total number of tiles is 5 + 5 + 6 + 4 = 20.
To find the probability, we divide the total number of favorable outcomes (blue tiles or tiles with the letter B) by the total number of possible outcomes (total number of tiles).
The total number of favorable outcomes is 9 + 10 = 19.
The probability is calculated as: favorable outcomes / total outcomes = 19 / 20 ≈ 0.95 or 95%.
p(Blue or B) = p(Blue) + p(B) – p(Blue and B).
= 9/(20)+ 9/20 - 4/20=14/20=.7
Probability of blue tile= 9/20
probability of letter b tile= 10/20= 1/2
Probability of blue or letter b= Probability of blue + probability of letter b
= 9/20 + 1/2
= 19/20