a bag is filled with 26 letter tiles, one for each letter in the alphabet. find the probability of choosing…

Explanation:

Step1: Count intersection elements

The intersection of curved and straight - letter tiles has 5 elements (B, D, P, Q, R).

Step2: Calculate first - draw probability

The probability of choosing a letter tile from the intersection on the first draw is $\frac{5}{26}$ since there are 5 favorable outcomes out of 26 total outcomes.

Step3: Calculate second - draw probability

Since there is no replacement, for the second draw, there are 4 favorable outcomes left out of 25 total outcomes. So the probability is $\frac{4}{25}$.

Step4: Calculate combined probability

The probability of both events occurring is the product of the probabilities of each event. So $P=\frac{5}{26}\times\frac{4}{25}$. $P = \frac{5\times4}{26\times25}=\frac{20}{650}=\frac{2}{65}$

Answer:

$\frac{2}{65}$