Soal dan Pembahasan Matematika Sukino Kelas XII Bab 4 LKS 2 Bag A no 1

Soal dan Pembahasan
Buku Sukino
Matematika Peminatan
Kelas XII
Bab 4 Distribusi dan Fungsi Peluang Binomial
Kunci Jawaban  Sukino

A

1. Sebuah uang logam dilempar sebanyak 5 kali dengan probabilitas munculnya gambar 0,6. Jika X menyatakan banyak muncul gambar dan Y menyatakan banyak muncul angka, tentukan rata-rata untuk X dan Y.


Jawaban :

p = probabilitas muncul gambar X = 0.6
q = probabilitas muncul angka Y = 1 - 0.6 = 0.4
n = 5

P(X = x ) = 5Cx . p^x q^5-x

P(X = x ) = 5Cx . 0.6^x 0.4^5-x

P(X = 0) = 5C0 . 0.6⁰ 0.4⁵= 1 . 1 . 0.01024 = 0.01024
P(X = 1) = 5C1 . 0.6¹ 0.4⁴= 5 . 0.6 . 0.0256 = 0.0768
P(X = 2) = 5C2 . 0.6² 0.4³= 10 . 0.36 . 0.064 = 0.2304
P(X = 3) = 5C3 . 0.6³ 0.4²= 10 . 0.216 . 0.16 = 0.3456
P(X = 4) = 5C4 . 0.6⁴ 0.4¹= 5 . 0.1296 . 0.4 = 0.2592
P(X = 5) = 5C5 . 0.6⁵ 0.4⁰= 1 . 0.07776 . 1 = 0.07776

Rata-rata X = 0 (0.01024) + 1 (0.0768) + 2 (0.2304) + 3 (0.3456) + 4 (0.2592) + 5 (0.07776)
= 0 + 0.0768 + 0.4608 + 1.0368 + 1.0368 + 0.3888

= 3

Rata-rata Y

P(Y = 5) = 5C0 . 0.6⁰ 0.4⁵= 1 . 1 . 0.01024 = 0.01024
P(Y = 4) = 5C1 . 0.6¹ 0.4⁴= 5 . 0.6 . 0.0256 = 0.0768
P(Y = 3) = 5C2 . 0.6² 0.4³= 10 . 0.36 . 0.064 = 0.2304
P(Y = 2) = 5C3 . 0.6³ 0.4²= 10 . 0.216 . 0.16 = 0.3456
P(Y = 1) = 5C4 . 0.6⁴ 0.4¹= 5 . 0.1296 . 0.4 = 0.2592
P(Y = 0) = 5C5 . 0.6⁵ 0.4⁰= 1 . 0.07776 . 1 = 0.07776

Rata-rata Y = 5 (0.01024) + 4 (0.0768) + 3 (0.2304) + 2 (0.3456) + 1 (0.2592) + 0 (0.07776)
= 0.0512 + 0.3072 + 0.6912 + 0.6912 + 0.2592
= 2


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