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4 coins are tossed simultaneously the expected number of head is?
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4 coins are tossed simultaneously the expected number of head is?
Expected Number of Heads in Tossing 4 Coins Simultaneously


Tossing a coin is a random experiment where the outcome is either head or tail. When 4 coins are tossed simultaneously, the possible outcomes are:



  • HHHH

  • HHHT

  • HHTH

  • HHTT

  • HTHH

  • HTHT

  • HTTH

  • HTTT

  • THHH

  • THHT

  • THTH

  • THTT

  • TTHH

  • TTHT

  • TTTH

  • TTTT



Out of these 16 possible outcomes, the number of heads varies from 0 to 4. The expected number of heads is the sum of the product of the number of heads in each outcome and their respective probabilities. The probability of an outcome is the product of the probabilities of each individual coin toss. Since the coins are fair, the probability of getting a head or a tail is 1/2.


Calculating the Expected Number of Heads


Let X be the number of heads in 4 coin tosses.


P(X = 0) = P(TTTT) = (1/2)^4 = 1/16

P(X = 1) = P(TTTH, TTHT, THTT, HTTT) = 4(1/2)^4 = 1/4

P(X = 2) = P(TTHH, THHT, HHTT, HTTH, THTH, HTHT) = 6(1/2)^4 = 3/8

P(X = 3) = P(HHHT, HHTH, HTHH, THHH) = 4(1/2)^4 = 1/4

P(X = 4) = P(HHHH) = (1/2)^4 = 1/16


Therefore, the expected number of heads is:


E(X) = 0(1/16) + 1(1/4) + 2(3/8) + 3(1/4) + 4(1/16) = 2

Therefore, the expected number of heads in tossing 4 coins simultaneously is 2.
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4 coins are tossed simultaneously the expected number of head is?
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