There are 30 psychiatrists and 24 psychologists attending a certain conference.

Question

There are 30 psychiatrists and 24 psychologists attending a certain

conference. Three of these 54 people are randomly chosen to take part in a panel

discussion. What is the probability that at least one psychologist is chosen?

I thought of going about this with

(30 C 1)(24 C 2) + (30 C 2)(24 C 1) + (30 C 3)(24 C 0).

Is this correct or what would be the correct way of thinking about this. My logic was assessing that we chose 1 out of 30 and the rest are 24 C 2, then continue by incrementing by 1.

Explanation / Answer

P( At least one psychologist) = ( 30C1 * 24C2 + 30C2 * 24C1 + 30C3 *24C0 ) / 54C3

= 0.9184

OR

P( At least one psychologist) = 1 - P( no psychologist)

= 1 - ( 24C3 / 54C3 )

= 1 - 0.0816

= 0.9184

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.