Question

Q. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. Find probability that it is
(i) Orange or red
(ii) Not red or blue
(iii) Not blue
(iv) Red, white or blue

Answer 1

Answer on Question #59818 – Math – Statistics and Probability

Question

A marble is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles. Find probability that it is

(i) Orange or red;

(ii) Not red or blue;

(iii) Not blue;

(iv) Red, white or blue.

Solution

Total amount of marbles is $10 + 30 + 20 + 15 = 75$. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue and 15 orange marbles

(i) Probability of the event ‘it is orange or red’ is

$$P = (15 + 10)/75 = 25/75 = 1/3 \approx 0.33.$$

(ii) Probability of the event ‘it is not red or blue (then it is white or orange)’ is

$$P = (30 + 15)/75 = 45/75 = 9/15 = 3/5 = 0.6.$$

(iii) Probability of the event ‘it is not blue (then it is red, white or orange)’ is

$$P(\text{‘it is not blue’}) = 1 - P(\text{‘it is blue’}) = 1 - 20/75 = (75 - 20)/75 = 55/75 = 11/15 \approx 0.733.$$

(iv) Probability of the event ‘it is red, white or blue’ is

$$P = (10 + 30 + 20)/75 = 60/75 = 12/15 = 4/5 = 0.8.$$

Answer: (i) 1/3; (ii) 0.6; (iii) 11/15; (iv) 0.8.

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