There are 9 Black pen, 5 red pen and 3 blue pen if 2 pen are selected blindly, find probability of getting both are red pen or blue pen.
1. 13/136
2. 13/304
3. 11/338
4. 15/288
1. 13/136
2. 13/304
3. 11/338
4. 15/288
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Correct Answer – Option 1 : 13/136
Given:
Black pen = 9
Red pen = 5
Blue pen = 3
Formula used:
nCr = n!/((n-r)! × r!)
Calculation:
Let S be the sample space then,
n(S) = number of way of selecting 2 pens out of 17 pens
⇒ n(S) = 17C2 = 17!/((17– 2)! × 2!)
⇒ (17 × 16)/2
⇒ 136
Let E be the event of getting both are red or blue pen
n(E) = 5C2 + 3C2
⇒ (5 × 4)/2 + (3 × 2)/2
⇒ 10 + 3
⇒ 13
P(E) = n(E)/n(S)
= 13/136
∴ The probability of getting both are red pen or blue pen is 13/136.