CTED TO VIDEO GAMES) An enge Cardinals, Dove, VID Question 2.6. (DO NOT GET game

Question

CTED TO VIDEO GAMES) An enge Cardinals, Dove, VID Question 2.6. (DO NOT GET game for kids. Inside the program he used five distinct birds, namely: Bluebird, Cardinals, Dove, Eagle, and Flamingo. The engineer allows only three birds to appear on the screen in a row and selection is made on purely random basis using a random number table. CardinalDove Eagle Fig. 2.6. Birds in the game. Bluebird Flamingo Amy plays the game on a computer, and she wonders: (a) What is the probability that same Bluebird will appear three times on the screen? Fig. 2.7. Amy (b) What is the probability that same bird will appear three times? (c) Assume the engineer did not allow for the same bird to appear three times, what is the probability that Bluebird, Dove and Flamingo will appear on the screen at the first, second and third places? 6T No help: Please do yourself

Explanation / Answer

(a)

Only 3 birds are shown in a row and each position (1st, 2nd and 3rd) can be occupied by either of the 5 birds

So all possible display of 3 birds can be in 5×5×5 = 125 ways

Therefore,

Probability that 3 Bluebirds will appear in a row 1/125 (1/5 × 1/5 × 1/5, as appearance of Bluebird in either of the 3 positions is 1/5)

(b)

Probability of same bird in each of the 3 position implies

Probability (3 Bluebirds or 3 Cardinals or 3 Doves or 3 Eagles or 3 Flamingoes)

Since each of the required events are independent

= P(3 Bluebirds) + P(3 Cardinals) + P(3 Doves) + P(3 Eagles) + P(3 Flamingoes)

= 1/125 + 1/125 + 1/125 + 1/125 + 1/125 + 1/125

= 5/125

= 1/25

(c)

If engineer does not repeat 3 birds the all possible cases = 125 - 5 = 120 cases

Now probability of particular case of Bluebird, Dove and Flamingo occupying positions 1, 2 and 3 will be 1/120 cases

(d)

As in (c) above if 3 birds do not appear consecutively there can be 120 possible cases

Now if Bluebird, Dove and Flamingo are to appear in random order, they may appear in 3! = 6 arrangements

So probability of these 3 birDs appearing is 6/120 = 1/20

(e)

If engineer does not allow appearance of a bird more than once on screen

Then all possible cases = 5×4×3 = 60 cases (as 1st position may be occupied by any of the 5 birds, 2nd position by any of the remaining 4 and 3rd position by any of the remaining 3 or 5P3)

Therefore, probability that Bluebird, Dove and Flamingo will occupy positions 1,2 and 3 respectively is 1/60

(f)

As in (e) above, there may be 60 possible cases

Probability of Bluebird, Dove and Flamingo appearing in random order is therefore 6/60 = 1/10,

(The 3 birds may arrange themselves in all possible 3! = 6 ways)

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