Multiple choice

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that (i) both balls are red. (ii) first ball is black and second is red. (iii) one of them is black and other is red.

  1. $0.56,\ 0.75,\ 0.67$
  2. $0.46,\ 0.56,\ 0.36$
  3. $0.56,\ 0.76,\ 0.76$
  4. $0.19,\ 0.24,\ 0.49$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 18. P(Black) = 10/18 = 5/9, P(Red) = 8/18 = 4/9. (i) Both Red: (4/9)(4/9) = 16/81 approx 0.197. (ii) Black then Red: (5/9)(4/9) = 20/81 approx 0.247. (iii) One Black, one Red: (5/9)(4/9) + (4/9)(5/9) = 40/81 approx 0.494. Option D matches these values.

AI explanation

With replacement, the probability of drawing a black ball is 10/18 and a red ball is 8/18. For part (i), both balls being red has a probability of 8/18 multiplied by 8/18, which equals 64/324 or approximately 0.19. For part (ii), the first ball being black and the second being red has a probability of 10/18 multiplied by 8/18, equalling 80/324 or approximately 0.24. For part (iii), getting one black and one red ball has a probability of 2 multiplied by 10/18 multiplied by 8/18, which gives 160/324 or approximately 0.49. These values match the respective probabilities of 0.19, 0.24, and 0.49.

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